{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gamma\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.rcParams['figure.figsize']=(7,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x142d5a20>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a1,a2,a3,b = 1.0,1.5,2.0,1.0\n",
    "x1=np.linspace(gamma.ppf(0.01,a=a1,scale=b),gamma.ppf(0.99,a=a1,scale=b),1000)\n",
    "x2=np.linspace(gamma.ppf(0.01,a=a2,scale=b),gamma.ppf(0.99,a=a2,scale=b),1000)\n",
    "x3=np.linspace(gamma.ppf(0.01,a=a3,scale=b),gamma.ppf(0.99,a=a3,scale=b),1000)\n",
    "\n",
    "plt.plot(x1,gamma.pdf(x1,a=a1,scale=b),linewidth=2,ls='-',label='a=1,b=1')\n",
    "plt.plot(x2,gamma.pdf(x1,a=a2,scale=b),linewidth=2,ls='--',label='a=1.5,b=1')\n",
    "plt.plot(x3,gamma.pdf(x1,a=a3,scale=b),linewidth=2,ls='-.',label='a=2,b=1')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
